|
%I #5 Mar 30 2012 18:57:54
%S 7,4,6,0,7,4,3,6,2,1,2,8,5,6,4,4,6,1,7,3,2,5,7,4,1,8,9,8,5,6,5,3,0,6,
%T 7,3,5,6,8,5,1,9,0,1,4,6,8,5,0,2,7,8,5,6,9,0,8,2,2,9,6,4,8,7,6,6,2,2,
%U 9,3,3,0,9,6,2,0,1,6,5,1,3,7,8,3,6,3,0,2,6,7,3,7,8,0,4,5,1,1,2
%N Decimal expansion of least x having 4*x^2+2x=cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: -0.7460743621285644617325741898565306735...
%e greatest x: 0.29900587455031735703746835072454193932...
%t a = 4; b = 2; c = 1;
%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t Plot[{f[x], g[x]}, {x, -1, 1}]
%t r1 = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A198357 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, .29, .30}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A198358 *)
%Y Cf. A197737.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 24 2011
|
